Disconnected (exported) mesh because of vertex paint?
There is a threshold value you can change when working with remove doubles.

There is two ways to change it. Both are (as blender standard) after you use the tool.

So first select all vertices (if you only want to join some, feel free to select a subset).



Now do Remove doubles. Probably nothing will happend because the threshold is way low by default. But in the toolbar (toggle it with T), at the bottom are the options for the last used tool. In this case it will look like this:



Simply change the Merge distance to snap together the desired vertices.



The second way to change this options is to press F6 directly after the tool. This brings up a dialog to do the same. It's a matter of personal taste what method you want to use. They are exactly the same in all other aspects.